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Distribution of responsibilities is a multi-task problem Sanjit Dhami (2005) Optimal Distribution of Powers In A Federation: A Simple, Unified Framework., University of Leicester, UK. Working Paper No. 05/24, July Two levels, four tasks: regional insurance, coarseness of federal information, internalisation of spillovers and raiding of commons. The paper examines six regimes of distribution of powers: autarky, centralization, unregulated devolution, regulated devolution, direct democracy, and revenue maximising leviathan. Theory

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Distribution of responsibilities is a multi-task problem Practice Geistlinger M. «Federalism and Distribution of Powers. The distribution of competences in the field of education» University of Salzburg, Department of Public Law. Geistlinger M. «Federalism and Distribution of Powers. The distribution of competences in the field of education» University of Salzburg, Department of Public Law. Survey across Federalist countries, including Russia. Survey across Federalist countries, including Russia. Ministry of Local Government and Regional Development (Norway). «The Governments recommendations» Ministry of Local Government and Regional Development (Norway). «The Governments recommendations» Responsibilities should be placed at the lowest effective level. Responsibilities should be placed at the lowest effective level. The county authority should not be developed into a superordinate authority. The county authority should not be developed into a superordinate authority. Changes in the distribution of responsibilities should help to reduce bureaucracy. Changes in the distribution of responsibilities should help to reduce bureaucracy. The central government should have the responsibility for standardized and rule – oriented responsibilities and for supervisory responsibilities. The central government should have the responsibility for standardized and rule – oriented responsibilities and for supervisory responsibilities.

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Planned Experiments of the Ministry 1. Organization of the County Governor and the county authority in a single administrative body – the single administration county authority 2. Differentiation of municipal responsibilities, which means that certain municipalities are assigned one or more county or state responsibilities. Testing the alternative models:

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A Federal State emerges by variety of reasons. Some of the reasons come from a general problem of control in complex multidimensional systems. See, for example: Qian Yingyi (1994) Incentives and Loss of Control in an Optimal Hierarchy. Review of Economic Studies, 61(3):

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The paper considers an commercial organization that owns a capital stock an uses a hierarchy to control the production. The optimal problem is to find number of tiers in the hierarchy and optimal quantity of workers is in each tier. The objective function is a revenue generated from production activity. The trade off is between the two parameters: the number of bureaucrats to control workers and efficiency of working activity under the control.

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There is sizable literature devoted to optimal design of technical devices, like memory for computers and others. See, for example: Jacob B. L., Chen P. M., Silverman S. R. and Mudge T. N. (1996) An Analytical Model for Designing Memory Hierarchies. IEEE Transactions of Computers, vol. 45, # 10, October Historically a Federal State appeared in a process of unification of relatively small states to be more powerful (militarily, politically economically) together. For example, there are Germany, Canada, USA. The opposite top – down process takes place too. It based on keeping multinational state sustainable.

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A fundamental problem for the necessity of federal states structure arises in relation with efficiency of provision of local and national public goods. See Besley T. and Coate Stephen (2003) Centralized versus decentralized provision of local public goods; a political economy approach Journal of Public Economics,

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In the presentation I formulate and solve relatively simple optimization problem where the only factor for Federal States existence matters. Namely, it is size of population. Notations: N - total number of citizens in a country; с - costs of a government to provide one unit of a public good (actually public service) per a person; q - number of a hierarchical level (a tier) for a given government; q = 0,1, 2, …; k q - costs for keeping functioning of the government on hierarchical level q, under condition that the level is lowest; n q - quantity of governments under subordination of the levels q government; f q - total costs for provision of a public service (quantity is equal to one) for the whole population plus costs to keep all governments functioning;

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Objective function – total costs (under conditions: (1) all citizens are equal to each other, (2) everybody receives a unit of the public service.) c*n 2 - costs for provision of a unit of public good (service) for n people; k q *ln(n q ) - costs to keep government of the level q functioning, under condition that the government controls n q governments of lower level Then if q = 0, one has total costs to provide one unit of public good and costs to keep the government functioning as f 0 = k 0 + c*N 2. Here the first term is costs of governments functioning (central one) and the second one is costs to provide public good for the whole population.

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If q >= 1 to calculate total costs is a little bit more difficult. It is easy to do under assumption that all governments of a given level control the same number of governments. The number n q indicate exactly that condition. The number does not depend on particular copy of the levels q government. Namely, f 1 = k 0 *ln(n 0 ) + n 0 *(k 1 + c*(N/n 0 ) 2 ) = k 0 *ln(n 0 ) + n 0 *k 1 + c*N 2 / n 0

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The problem consists of finding the q*, which provides minimal total costs for provision of public good in quantity 1. In other words: q* = arg Min(f q ) Here Min is taken over q. But it is clear that functions f q depend on the other parameters participating in the definition of the function, that is on N, с, k q, n q. Hence the number q* depends on the named parameters. Optimal number of governments levels (tiers)

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Optimal quantity of inhabitances in a country What is more effective from the point of view of total costs to provide public goods? To be in large Federal State or to create smaller state (probably federal one too). Much depends on relation between the numbers k q. The population has to compare the total costs (and hence amount of taxes) under staying in the initial Federation or secession in a certain stake. Namely, one has to compare {Min(f q )/n}, where n runs from 1 to N. The N can be equal to infinity. Min is taken over n and q. Here Min(f q )/n is a head tax in the case of the size of population is equal to n. The country has federal structure if q*>0.

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Optimal size of a country with a fixed number of ties Let us suppose that q is given. Then optimal size of population n * (q) is going to be dependent on the given q. The problem makes sense in some practical issues as we see below.

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Russian Federation Formally according to the Constitution of Russian Federation there are three levels: Federal government 1 Subjects of Federation 89 Municipalities In fact Russia has or will have soon five (six) levels: Federal government 1 Federal districts 7 Subjects of Federation 89 (87) Municipal districts Townships Villages The reform of the local governance considers creating townships and villages in total. The townships and villages are at the same level but with a little bit different status.

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Alesina Alberto and Spolaore Enrico (1997), On the Number and Size of Nations, The Quarterly Journal of Economics, CXII, #4, November 1997, pp McGuckin R. and Dougherty S. (2003) Restructuring Chinese Enterprises: The Effect of Federalism and Privatization Initiatives on Business Performance. The Conference Board Research Report R RR

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Besley T. and Coate Stephen (2003) Centralized versus decentralized provision of local public goods; a political economy approach Journal of Public Economics, Besley T. and Coate Stephen (2003) Centralized versus decentralized provision of local public goods; a political economy approach Journal of Public Economics, Bewley Truman F. (1981) A Critique of Tiebouts Theory of Local Public Expenditures. Econometrica, vol. 49, #3, May, Bewley Truman F. (1981) A Critique of Tiebouts Theory of Local Public Expenditures. Econometrica, vol. 49, #3, May, McGuckin R. and Dougherty S. (2003) Restructuring Chinese Enterprises: The Effect of Federalism and Privatization Initiatives on Business Performance. The Conference Board Research Report R RR. McGuckin R. and Dougherty S. (2003) Restructuring Chinese Enterprises: The Effect of Federalism and Privatization Initiatives on Business Performance. The Conference Board Research Report R RR.